如何计算多边形主延伸方向与X轴的夹角？排查计算异常

已知任意简单凸/凹多边形的顶点坐标与质心，需计算其主延伸方向与参考系X轴的夹角。示例里蓝色线是多边形主延伸方向，黄色圆代表质心，红色圆是多边形中点。

我尝试通过计算协方差矩阵最大特征值对应的特征向量来求解，多数测试场景下结果有效，但某一多边形的计算结果约为80°，和预期的0°不符，不确定是数学逻辑出错还是C#代码实现有问题，相关代码如下：

// Returns the angle between the x-axis and the line along which the figure extends mainly.
public double GetOrientation()
{
    Point centroid = this.GetCentroid(); // Centroid of the polygon.
    int vertexesNumber = this.GetVertexesNumber(); // Number of vertexes of the polygon.
    double covXX = 0.0; // Variance of x, indicates how much x varies from the mean.
    double covYY = 0.0; // Variance of y, indicates how much y varies from the mean.
    double covXY = 0.0; // Covariance between x and y, indicates how much x and y vary together.

    // Calculates the covariance matrix, indicates how the vertexes are distributed with respect to the centroid.
    foreach (Point vertex in vertexes) // For each vertex of the polygon.
    {
        double x = vertex.X - centroid.X; // Calculates the difference of the vertex at x from the centroid at x.
        double y = vertex.Y - centroid.Y; // Calculates the difference of the vertex at y from the centroid at y.
        covXX += x * x; // Adds the square of the deviation from x to the centroid.
        covYY += y * y; // Adds the square of the deviation from y to the centroid.
        covXY += x * y; // Adds the product of deviations from x and y.
    }
    covXX /= vertexesNumber; // Calculates the mean of the variance along x.
    covYY /= vertexesNumber; // Calculates the mean of the variance along y.
    covXY /= vertexesNumber; // Calculates the mean of the covariance between x and y.

    double tr = covXX + covYY; // Calculates the trace of the matrix.
    double det = covXX * covYY - covXY * covXY; // Calculates the determinant of the matrix.

    double lambda = (tr + Math.Sqrt(tr * tr - 4 * det)) / 2; // Calculates the greatest eigenvalue of the matrix.
    double a1 = covXY; // Calculates the component along the x-axis of the eigenvector associated with the greatest eigenvalue.
    double a2 = lambda - covXX; // Calculates the component along the y-axis of the eigenvector associated with the greatest eigenvalue.

    double angle = Math.Atan2(a2, a1); // Calculates the angle between the x-axis and the line along which the polygon extends mainly, defined by the vector a1, a2.
    angle *= 180.0 / Math.PI; // Converts the angle from radians to degrees.

    return angle;
}

内容的提问来源于stack exchange，提问作者user28277546